Question

Arun speaks the truth 4 out of 5 times, and bhavana speaks the truth 6 out of 7 times.what is the probability that they will contradict each other in stating the same fact

Answer 1

Arun speaks truth 4/5 times.
Bhavana speaks truth 6/7 times
Take the lcm of 5 and 7
= 35
So,
4/5 = 28/35
6/7 = 30/35
So, arun lies 7/35 times and bhavana lies 5/35 times so bhavana speaks truth 2 more times and that time arun will lie so they will contradict each other 2/35 times.
Hope it helps....

Answer 2

Answer:

$\textbf{Hence, The probability that they will contradict each other = }\bf\frac{2}{35}$

Step-by-step explanation:

Arun speaks the truth 4 out of 5 times

$\implies\text{Probability that Arun speaks truth = }\frac{4}{5}$

bhavana speaks the truth 6 out of 7 times

$\implies\text{Probability that Bhawna speaks truth = }\frac{6}{7}$

Making denominator same of both the probabilities

$\implies\frac{28}{35}\text{ and }\frac{30}{35}$

So, Arun speak lie 7 times and Bhawna speak lie 5 times

⇒ Arun speak lie 2 times more than that of Bhawna

$\textbf{Hence, The probability that they will contradict each other = }\bf\frac{2}{35}$